Adaptive non-parametric efficiency frontier analysis: a neural-network-based model

Abstract

There have been two schools of efficiency analysis for private and public organizations. One is the data envelopment analysis (DEA) method which is based on a mathematical programming approach, and the other is the estimation of stochastic frontier functions (SFF) which is based on the econometric regression theory. Each of these two methodologies has its strength as well as major limitations. This paper proposes a non-parametric efficiency analysis method based on the adaptive neural network technique. The proposed computational method is able to find a stochastic frontier based on a set of input–output observational data. Like SFF, the proposed method considers two types of deviations involved in input–output data: managerial (external) and observational (internal) deviations. Like DEA, the proposed method does not require explicit assumptions about the function structure of the stochastic frontier. However, unlike any SFF and stochastic DEA methods, the proposed method does not require any parametric assumption of distribution functions. Using the neural networks, this method provides an adaptive way of obtaining empirical estimates of stochastic frontiers. An example using real data is presented for illustrative purposes. Simulation experiments demonstrate that the neural-network-based method would be effective as adaptive non-parametric efficiency analysis. Scope and purpose Efficiency frontier analysis has been an important approach of evaluating firms’ performance in private and public sectors. There have been many efficiency frontier analysis methods reported in the literature. However, the assumptions made for each of these methods are restrictive. Conflicting conclusions of efficiency are often resulted by using the different methods due to the untestability of the assumptions. This study proposes a non-parametric efficiency frontier analysis method based on the adaptive neural network technique. The assumptions used for the proposed adaptive non-parametric method are no more than two universally accepted axioms of efficiency frontiers. First, the efficiency frontier is concave. Second, the external deviation in data has a one-sided distribution, and the internal deviation in data has a two-sided distribution.